The cost to manufacture a waterbottle is a proportional relationship. This relationship is shown in the table. bottles manufactured (x) 0 25 50 100 cost in dollars (y) 0 20 40 80 What is the constant of proportionality for the data in the table?
To find the constant of proportionality, we need to determine the ratio of the cost to the number of bottles manufactured.
The ratio of the cost to the number of bottles manufactured remains constant in a proportional relationship.
Let's calculate the ratio for the given data:
For x = 0, y = 0, the ratio is 0/0, which is undefined.
For x = 25, y = 20, the ratio is 20/25 = 0.8.
For x = 50, y = 40, the ratio is 40/50 = 0.8.
For x = 100, y = 80, the ratio is 80/100 = 0.8.
As we can see, the ratio of the cost to the number of bottles manufactured is always 0.8.
Therefore, the constant of proportionality for the data in the table is 0.8.
To find the constant of proportionality, we need to find the ratio of the change in y (cost) to the corresponding change in x (number of bottles manufactured).
Let's find the change in y and the change in x for two data points from the given table:
For the first two data points:
Change in y = 20 - 0 = 20
Change in x = 25 - 0 = 25
So, the ratio of the change in y to the change in x is 20/25 = 0.8.
We can check if this ratio holds for the other two data points as well:
For the second and third data points:
Change in y = 40 - 20 = 20
Change in x = 50 - 25 = 25
Again, the ratio of the change in y to the change in x is 20/25 = 0.8.
Lastly, for the third and fourth data points:
Change in y = 80 - 40 = 40
Change in x = 100 - 50 = 50
Once again, the ratio of the change in y to the change in x is 40/50 = 0.8.
Since the ratio of the change in y to the change in x is the same for all the data points, we can conclude that the constant of proportionality for this table is 0.8.
To find the constant of proportionality, we need to determine the ratio between the cost and the number of bottles manufactured. In other words, we need to calculate the unit rate.
Let's choose any two points from the table. For example, we can choose the first and the second data points.
First data point: (0, 0)
Second data point: (25, 20)
To calculate the constant of proportionality, we divide the change in "cost" by the change in "bottles manufactured." In this case, the change in cost is 20 - 0 = 20, and the change in bottles manufactured is 25 - 0 = 25.
Constant of proportionality = (change in cost) / (change in bottles manufactured)
Constant of proportionality = 20 / 25
Constant of proportionality = 0.8
Therefore, the constant of proportionality for the given data is 0.8.